Benedetti, Giovanni Battista de, Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]

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            <div xml:id="echoid-div293" type="appendix" level="3" n="1">
              <p>
                <s xml:id="echoid-s1341" xml:space="preserve">
                  <pb o="104" rhead="IO. BAPT. BENED." n="116" file="0116" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0116"/>
                producitur ex
                  <var>.i.e.</var>
                differentia in
                  <var>.i.n.</var>
                aggregatum amborum numerorum, ſed hoc pro
                  <lb/>
                ductum excedit productum
                  <var>e.c</var>
                : partem gnomonis dicti per
                  <var>.u.n.</var>
                quod quidem
                  <var>.u.
                    <lb/>
                  n.</var>
                æquatur ipſi
                  <var>.u.o.</var>
                reliquæ ſcilicet parti ipſius gnomonis,
                  <reg norm="nam" type="context">nã</reg>
                  <var>.e.u.</var>
                æqualis eft
                  <var>.i.c.</var>
                qua
                  <lb/>
                re et
                  <var>.a.i.</var>
                ſed
                  <var>.e.t.</var>
                ęquatur
                  <var>.e.a.</var>
                vnde
                  <var>.t.u.</var>
                æqualis erit
                  <var>.e.i.</var>
                </s>
                <s xml:id="echoid-s1342" xml:space="preserve">quare et
                  <var>.u.c</var>
                : at cum
                  <var>.c.n.</var>
                æqua
                  <lb/>
                lis ſit ipſi
                  <var>.a.e.</var>
                erit etiam æqualis ipſi
                  <var>.
                    <lb/>
                  o.t</var>
                . </s>
                <s xml:id="echoid-s1343" xml:space="preserve">quare
                  <var>.u.n.</var>
                æqualis erit ipſi
                  <var>.u.o.</var>
                  <lb/>
                & tunc intellectus quieſcit, &
                  <reg norm="abſque" type="simple">abſq;</reg>
                  <lb/>
                  <figure xlink:label="fig-0116-01" xlink:href="fig-0116-01a" number="159">
                    <image file="0116-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0116-01"/>
                  </figure>
                aliqua alia experientia verè ſcientifi
                  <lb/>
                  <reg norm="ceque" type="simple">ceq́;</reg>
                dicere poteft, quòd.</s>
              </p>
              <p>
                <s xml:id="echoid-s1344" xml:space="preserve">Quorumcumque duorum nume-
                  <lb/>
                rorum differentia, fi fuerit multipli-
                  <lb/>
                cata in aggregatum eorum, producit
                  <lb/>
                ipſam
                  <reg norm="differentiam" type="context">differentiã</reg>
                , quæ eftinter qua-
                  <lb/>
                drata eorum.</s>
              </p>
              <p>
                <s xml:id="echoid-s1345" xml:space="preserve">Hæcautem propoſitio à me ipſo
                  <lb/>
                etiam in .60. </s>
                <s xml:id="echoid-s1346" xml:space="preserve">Theoremate huius libri
                  <lb/>
                aliter demonftrata fuit.</s>
              </p>
              <p>
                <s xml:id="echoid-s1347" xml:space="preserve">DE ſpeculatione autem, etſcientia ſecundi exempli, in ſecunda hic ſubſcripta
                  <lb/>
                figura
                  <var>.ω.</var>
                cogitemus lineam
                  <var>.u.a.</var>
                tribusin partibus arithmeticè diuiſam, qua
                  <lb/>
                rum maxima ſit
                  <var>.u.o.</var>
                media. ſit
                  <var>.o.e.</var>
                minima verò ſit
                  <var>.e.a.</var>
                multiplicatio autem mediæ
                  <var>.
                    <lb/>
                  o.e.</var>
                in ſe ſit quadratum
                  <var>.o.t.</var>
                abſcindatur deinde ex
                  <var>.o.e</var>
                :
                  <var>e.i.</var>
                æqualis
                  <var>.e.a.</var>
                </s>
                <s xml:id="echoid-s1348" xml:space="preserve">tunc
                  <var>.o.i.</var>
                erit
                  <lb/>
                differentia inter
                  <var>.o.e.</var>
                et
                  <var>.e.a.</var>
                & æqualis differentiæ inter
                  <var>.o.e.</var>
                et
                  <var>.o.u.</var>
                ex hypotefi, quæ
                  <lb/>
                quidem
                  <var>.o.i.</var>
                in ſe ducta procreabit quadratum
                  <var>.o.c.</var>
                quod erit productum ex differen
                  <lb/>
                tijs ipſarum partium, & erit pars quadrati
                  <var>.o.t.</var>
                ſuperius dicti, vt exſe patet. </s>
                <s xml:id="echoid-s1349" xml:space="preserve">Nunc
                  <lb/>
                autem dico gnomonem
                  <var>.i.t.n.</var>
                æqualem eſſe ei quod fit ex
                  <var>.a.e.</var>
                in
                  <var>.o.u</var>
                . </s>
                <s xml:id="echoid-s1350" xml:space="preserve">Producatur igi
                  <lb/>
                tur
                  <var>.e.t.</var>
                quouſque
                  <var>.t.r.</var>
                æqualis ſit ipſi
                  <var>.o.i</var>
                . </s>
                <s xml:id="echoid-s1351" xml:space="preserve">tunc
                  <var>.e.r.</var>
                erit æqualis
                  <var>.o.u.</var>
                quod etiam clarum
                  <lb/>
                eſt. </s>
                <s xml:id="echoid-s1352" xml:space="preserve">Claudatur ergo rectangulum
                  <var>.i.r.</var>
                quod erit æquale producto ipſius
                  <var>.e.a.</var>
                in
                  <var>.o.u.</var>
                  <lb/>
                Nam
                  <var>.e.i.</var>
                ſumpta fuit
                  <lb/>
                æqualis
                  <var>.e.a.</var>
                ſed ex ra
                  <lb/>
                  <figure xlink:label="fig-0116-02" xlink:href="fig-0116-02a" number="160">
                    <image file="0116-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0116-02"/>
                  </figure>
                tionibus in priori
                  <reg norm="exem" type="context">exẽ</reg>
                  <lb/>
                plo allatis,
                  <reg norm="productum" type="simple">ꝓductum</reg>
                  <var>.
                    <lb/>
                  i.r.</var>
                æquale erit gno-
                  <lb/>
                moni
                  <var>.i.t.n</var>
                . </s>
                <s xml:id="echoid-s1353" xml:space="preserve">Nuncau
                  <lb/>
                tem verè, ſcientifice-
                  <lb/>
                q́ue poſſumus affirma
                  <lb/>
                re, quòd. </s>
                <s xml:id="echoid-s1354" xml:space="preserve">Datis tribus
                  <lb/>
                numeris
                  <reg norm="ſecundum" type="context">ſecundũ</reg>
                pro
                  <lb/>
                greffionem arithme-
                  <lb/>
                ticam diſpofitis, fa-
                  <lb/>
                cit multiplicatio me-
                  <lb/>
                dij in ſe quantum mul
                  <lb/>
                tiplicatio extremorum inter ſe, cum multiplicatione differentiarum inter ſe.</s>
              </p>
              <p>
                <s xml:id="echoid-s1355" xml:space="preserve">Et ſic de alijs huiuſmodi inuentionibus infero.</s>
              </p>
              <p>
                <s xml:id="echoid-s1356" xml:space="preserve">DIcturus igitur aliquid circa
                  <reg norm="regulam" type="context">regulã</reg>
                falſi, videtur mihi nullam oportere facere
                  <lb/>
                mentionem de origine huiuſcæ regulæ, cum in hoc Stifelius ſatisfecerit, ſed </s>
              </p>
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